Office: Armstrong Hall 408H

Office Hours: MW 11:30am-12:30pm, and by appointment

Class Meetings: TuTh 1:00pm-2:15pm in Armstrong Hall 313

No. | Date | Class Summary | Sections(s) | Comments |

1 | Aug 17 | Introduction; Induction; the sum 1 + ... + n |
1-1 | HW1 assigned. |

2 | Aug 22 | Basis representation | 1-2 | |

3 | Aug 24 | Euclid's Division Lemma; GCDs; Integer Combinations | 2-1 | - |

4 | Aug 29 | Extended Euclidean Algorithm; primes | 2-2 | - |

5 | Aug 31 | Linear Diophantine Eqns; Fundamental Theorem of Arithmetic | 2-3,2-4 | HW1 due; HW2 assigned. |

6 | Sep 5 | Permutations and Combinations | 3.1,3.2 | - |

7 | Sep 7 | Fermat's little theorem; Wilson's theorem | 3.2,3.3 | - |

8 | Sep 12 | Congruences; Complete and Reduced Residue Systems | 4.1,4.2 | - |

9 | Sep 14 | Riffling (congruence application); Linear congruence relations | 4.3,5.1 | HW2 due; HW3 assigned. |

10 | Sep 19 | Euler's Theorem; Fermat and Wilson II | 5.2 | - |

11 | Sep 21 | Systems of congruences; Chinese remainder theorem; Polynomial congruences | 5.3,5.4 | - |

12 | Sep 26 | Combinatorial study of Euler's phi function | 6.1 | - |

13 | Sep 28 | Multiplicative functions; Dirichlet product | 6.2-6.4 | HW3 due; HW4 assigned. |

14 | Oct 3 | Mobius inversion | 6.4 | - |

15 | Oct 5 | Midterm Exam (coverage up to and including Thurs Sept 28) | - | Midterm (pdf) |

16 | Oct 10 | Orders modulo m and primitive roots |
7.1 | - |

17 | Oct 12 | Existence of primitive roots modulo a prime; prime counting function | 7.2,8.1 | - |

18 | Oct 17 | Divergence of Sum 1/p, Chebychev's Thm | 8.2 | HW4 due. |

19 | Oct 19 | Bertrand's postulate | 8.2 | HW5 assigned. |

20 | Oct 24 | Open problems about primes; Euler's Criterion; Legendre Symbol | 8.2,9.1,9.2 | - |

21 | Oct 26 | Gauss's Lemma; Legendre symbols (-1/p) and (2/p) | 9.3 | - |

22 | Oct 31 | Quadratic Reciprocity Law I | 9.3 | - |

23 | Nov 2 | Quadratic Reciprocity Law II | 9.3,9.4 | HW5 due; HW6 assigned. |

24 | Nov 7 | Consecutive quadratic residue pairs | 10.1 | - |

25 | Nov 9 | Consecutive quadratic residue triples I | 10.2 | - |

26 | Nov 14 | Consecutive quadratic resuide triples II | 10.2 | - |

27 | Nov 16 | Numbers representable as the sums of two squares | 11.1 | HW6 due; HW7 assigned. |

28 | Nov 28 | Partitions | 12.1 | - |

29 | Nov 30 | Generating functions; Partition identities | 13.1 | - |

30 | Dec 5 | Geometric number theory | 15 | - |

- | Dec 13 | Final Exam: Wed Dec 13 11am to 1pm | - | - |

milans@math.wvu.edu